GV-Spectroscopy for F-theory on genus-one fibrations

TL;DR

The paper introduces GV-spectroscopy, a new technique for systematically constructing F-theory models with desired gauge groups by calculating fiber Gopakumar-Vafa invariants, improving efficiency especially for complex fibers.

Contribution

It presents GV-spectroscopy, a novel method leveraging mirror symmetry and the Frobenius method to analyze fiber invariants in F-theory compactifications, enabling base-independent matter locus calculations.

Findings

GV-spectroscopy efficiently analyzes complex fiber structures.

Constructed F-theory models with specific gauge groups and spectra.

Confirmed anomaly cancellation in studied supergravity models.

Abstract

We present a novel technique to obtain base independent expressions for the matter loci of fibrations of complete intersection Calabi-Yau onefolds in toric ambient spaces. These can be used to systematically construct elliptically and genus one fibered Calabi-Yau $d$-folds that lead to desired gauge groups and spectra in F-theory. The technique, which we refer to as GV-spectroscopy, is based on the calculation of fiber Gopakumar-Vafa invariants using the Batyrev-Borisov construction of mirror pairs and application of the so-called Frobenius method to the data of a parametrized auxiliary polytope. In particular for fibers that generically lead to multiple sections, only multi-sections or that are complete intersections in higher codimension, our technique is vastly more efficient than classical approaches. As an application we study two Higgs chains of six-dimensional supergravities that are engineered by fibrations of codimension two complete intersection fibers. Both chains end on a vacuum with $G=\mathbb{Z}_4$ that is engineered by fibrations of bi-quadrics in $\mathbb{P}^3$. We use the detailed knowledge of the structure of the reducible fibers that we obtain from GV-spectroscopy to comment on the corresponding Tate-Shafarevich group. We also show that for all fibers the six-dimensional supergravity anomalies including the discrete anomalies generically cancel.